Military science has for millennia tried to study and maximize a fighting force’s advantages in battle. However,
it has never employed mathematical tools in its analysis. Constructal theory provides a means to understand
the optimal placement, structure, and deployment of phalanx based armies. Because phalanxes posses a direct
geometric correlation between strength and vulnerability, their form is well suited to theoretical analysis. The
optimum phalanx formation is given as one that minimizes exposed flanks while maximizing the unit’s effective
front and deployment depth. In a further example, a given hypothetical distribution of fast, slow, and
medium troops charts the development and evolution of flanking maneuvers and ultimately Hannibal’s double
envelopment strategy at Cannae.